Getting feedback from an adcom is sort of like asking your ex- why he/she broke up with you.
It'll come down to one of three things:
(1) It's obvious and specific (which you know already) - for example if you know that your GMAT sucked or you were too young/too old, then that was probably a big factor
(2) It's something they're not willing to say because it will be too hurtful or insulting (i.e. you were boring/dull, you came across as a dork or a douche) - none of these value judgments will really help you; yes they're subjective value judgments, but that's what it comes down to when there's way more people of a similar caliber than there are seats available
(3) They can't really pinpoint specifics; they just *know* they've lost interest (in admissions, oftentimes it's not some specific thing they can identify; it's just that they liked other applicants more than you).
Admissions as you know is a very subjective process. They're trying to choose a subset of folks from a pool of people who are very comparable in caliber.
It's not some scientific process where adcoms are notating or justifying their decision in excruciating detail. They can reject you or accept you for ANY reason or NO reason - and as a result the written feedback on the application could be detailed or cryptic - either way, their decision is final.
Again, admissions is NOT an analytical, scientific process (and it really can't be, unless you want b-school to be even more douchey than its reputation already is to non-MBAs in the working world). It's based more on feel and instinct than the adcoms would ever want to publicly admit.
So unless if it's blindingly obvious (i.e. your GMAT was way below average), then they're not willing to say stuff that could come across as insulting or hurtful.
In many respects, it's analogous to dating -- with the adcom being the woman and the applicant the man. Sometimes, there's specific reasons why the gal will run away from you. Other times, there's nothing wrong with you that she could identify - she just found another guy who she liked more.